We should compare our physical system with related phenomena. The key elements of our design include: a relativistic charge cluster of a huge number, a quantum oscillator of relatively large spatial extension and low frequency, and adiabatic conditions for the oscillator to complete transient spontaneous radiation during the interacting period. These elements have been encountered individually in some studies. For example, Coulomb excitation [1]}, [2]} may also utilize a relativistic projectile, but in a perturbative and/or non-adiabatic way. The AC-stark[3]} effect may be adiabatic and non-perturbative, but the electric field is from an electromagnetic wave, not relativistic particles. The term “strong-field” typically refers to an intensive laser field, not a relativistic Coulomb field. It is our study that combines all these key elements, and brings sharply a “Coulomb-type” gauge dependence. We invent this terminology to refer to the gauge-choice problem for the Coulomb field of charged particles, especially relativistic ones. Naturally, the gauge-choice problem for an electromagnetic wave or the vacuum field may be termed “Lamb-type”.
